Galois symmetries of the stable homology of integer symplectic groups
When: October 22, 2020
4:30 pm - 5:30 pm
Where: Virtually
Speaker: Akshay Venkatesh - Institute for Advanced Study
There are many natural sequences of moduli spaces in algebraic geometry whose homology approaches a “limit”, despite the fact that the spaces themselves have growing dimension. If these moduli spaces are defined over a field K, this limiting homology carries an extra structure — an action of the Galois group of K — which is arithmetically interesting.
In joint work with Feng and Galatius, we compute this action (or rather a slight variant) in the case of the moduli space of abelian varieties. I will explain the answer and why I find it interesting. No familiarity with abelian varieties will be assumed — I will emphasize topology over algebraic geometry.